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10/28/09 - Rotational Kinetic Energy and Angular Momentum
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  | Translational Kinetic Energy
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  | The kinetic energy we've talked about previously, (1/2)mv2, is called translational kinetic energy because it assumes an object is "sliding" or otherwise moving without rotation.

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  | Rotational Kinetic Energy
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  | The kinetic energy associated with rotation is called, of course, rotational kinetic energy and it depends on the moment of inertia I and the angular velocity ω. Specifically, rotational kinetic energy can be expressed as (1/2)Iω2. Remember that I is related to mR2 and ω = v/R, so it's possible to express rotational energy in terms of m and v2, but the constant won't usually be 1/2.

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  | If we start an object moving and there is no unbalanced force acting on it, we expect it to move with constant speed in a straight line. It won't speed up or slow down or change direction. That's Newton's first law, called the law of inertia.
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  | We find analogous behavior when we start something spinning. If no unbalanced torque acts on it, we expect it to continue spinning with constant angular velocity. Again, it won't speed up or slow down or tilt in a different direction. This is the concept of angular momentum.
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  | For a point mass moving at velocity v perpendicular to the radius R from a point of rotation, we say the angular momentum L is mvR. For an extended object, instead, we say the angular momentum L is Iω.
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  | A figure skater may start spinning with her arms held out to the sides. As she pulls her arms in (or puts them over her head), she reduces her moment of inertia and her angular velocity increases, causing her to spin faster. When she wants to slow down, she can extend her arms or legs to increase her moment of inertia or dig her skate into the ice away from the point of rotation to exert an external torque to change her angular momentum.
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  | Read pp. 279-293 of the text.
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